I have a 2 ton split AC that would draw about 12A current and is rated for 2260W input power at 230V. With this much information how do I choose a solid state relay? Since the Rating is in inductive what do I look for?
Nothing special is needed. You can buy a SSR without zero-cross detector for rated current, let's say 25A or more. Parallel at the output you should install aditional snubber network, that is a resitor and capacitor in series. Zero-cross SSR isn't a good choice for inductive loads, while a circuit withoust snubber can have problems while turning off.
About different types of SSR and their applications: http://www.crydom.com/en/tech/newsletters/solid%20statements%20-%20ssrs%20switching%20types.pdf
Inductive loads are hard on relays during turnoff.Relays that that are specified for motors are available and have a HORSEPOWER rating as well as a voltage and current rating .When the relay states a motor horsepower rating you cant go wrong .These good relays are more expensive and are physicaly larger and have generous contact spacing and are often referred to as contactors .You can go solid state if you know what you are doing .For safety there should be a mechanical contact in series with the SSR contact .For disipation reasons there should be a contact in paralell with SSR contact.The SSR aproach has been shown to be more complicated than the simple mechanical approach .The SSR way may have to be considered if your job involves a large number of switching operations.Fortunately the manufacturers of mechanical switchgear state number of operations Vs current at inductive loads .